Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √0.252 + 0.42 - 2·0.25·0.4·cos(150°)
= √0.0625 + 0.16 - 0.2·-0.866
= √0.3957
= 0.629
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(150°))
= arcsin(0.3975·0.5)
= 11.46°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(150°))
= arcsin(0.6359·0.5)
= 18.54°
Периметр:
P = a + b + c
= 0.629 + 0.25 + 0.4
= 1.279
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√0.6395·(0.6395-0.629)·(0.6395-0.25)·(0.6395-0.4)
=√0.6395 · 0.0105 · 0.3895 · 0.2395
=√0.0006263871324375
= 0.02503
Высота :
ha =
=
= 0.07959
hb =
=
= 0.2002
hc =
=
= 0.1252